The efficiency of electron acceleration in collisionless shocks and gamma-ray burst energetics Academic Article uri icon


  • Afterglow observations are commonly used to determine the parameters of GRB explosions, the energy E, surrounding density n, postshock magnetic field equipartition fraction B, and electron equipartition fraction e, under the frequently made assumption that the efficiency of electron "injection" into relativistic shock acceleration is high, i.e., that the fraction f of electrons that undergo acceleration is f ≈ 1. We show that the value of f cannot be determined by current observations, since currently testable model predictions for a parameter choice {E' = E/f, n' = n/f, = fB, = fe} are independent of the value of f for me/mp ≤ f ≤ 1. Current observations imply that the efficiency f is similar for highly relativistic and subrelativistic shocks and plausibly suggest that f ~ 1, quite unlike the situation in the Crab Nebula. However, values me/mp ≤ f 1 cannot be ruled out, implying a factor me/mp uncertainty in determination of model parameters. We show that early, ≤10 hr, radio afterglow observations, which will be far more accessible in the Swift era, may provide constraints on f. Such observations will therefore provide a powerful diagnostic of GRB explosions and of the physics of particle acceleration in collisionless shocks.

publication date

  • January 1, 2005